1. APES 1st Semester Math Review
2015
APES mastering the math part 1 video
APES mastering the math part 2 video

2. Comparing the value of two washing machines.
An average family washes 5 loads of laundry per week. How many loads does the family wash in a year?

3. Comparing the value of two washing machines.
An average family washes 5 loads of laundry per week. How many loads does the family wash in a year?
5 loads x 52 weeks = load
Week Year Year

4. A traditional machine uses 150 L of water per load of laundry and the efficient machine uses 75 L. How many liters would the efficient washing machine save per year?

5. A traditional machine uses 150 L of water per load of laundry and the efficient machine uses 75 L. How many liters would the efficient washing machine save per year?
(150 L – 75L)/load x 260 loads/year = 19,500 L/year

6. The average cost of water in the Unites States is $0
The average cost of water in the Unites States is $0.40 for every 1,000 L. How much money would you save each year by using the more efficient washing machine?

7. The average cost of water in the Unites States is $0
The average cost of water in the Unites States is $0.40 for every 1,000 L. How much money would you save each year by using the more efficient washing machine?
$0.40/1000 L x 19,500 L /year = $7.80 /year

8. How many years would you have to own the more efficient machine that cost $800 before you save money compared to the traditional machine that cost $400?

9. How many years would you have to own the more efficient machine that cost $800 before you save money compared to the traditional machine that cost $400?
$800 - $400 = 51.3 years $7.80/year Is this a big enough economic incentive to save water for most people? What are the ecological benefits for saving water?

10. An older showerhead uses 150L for a 10 minute shower, whereas a reduced flow showerhead uses only 95L. If you take one shower per day, how many liters of water would you save in 1 year if you replaced your older showerhead?

11. An older showerhead uses 150L for a 10 minute shower, whereas a reduced flow showerhead uses only 95L. If you take one shower per day, how many liters of water would you save in 1 year if you replaced your older showerhead?
Old shower – New shower = 150L per day– 95L per day = 55L per day
55L/day x 365 days per year = 20,075 liters

12. Tropical Rainforests are being cleared at 32,500 hectares per day
Tropical Rainforests are being cleared at 32,500 hectares per day. A hectare is an area that is 10,000 square meters. A soccer field is 6,500 square meters. How many soccer fields of rainforest are being cleared a day?

13. Tropical Rainforests are being cleared at 32,500 hectares per day
Tropical Rainforests are being cleared at 32,500 hectares per day. A hectare is an area that is 10,000 square meters. A soccer field is 6,500 square meters. How many soccer fields of rainforest are being cleared a day?
32,500 hectares x 10,000 m2 = 325,000,000 m2
hectare
325,000,000 m2 x 1 soccer field = 50,000 soccer fields
6,500 m2

14. Describe 3 negative environmental effects associated with the removal of so much rainforest per day.

15. Removal of trees removes habitat for animals like insects, birds and small mammals. These organisms are prey for larger animals. If the trees are taken away these small organisms cannot survive and will impact the size of the populations of larger organisms because larger organisms will have less to eat.
Trees take in carbon dioxide and release oxygen. If the trees are removed, there will be less oxygen in the air and more carbon dioxide in the air. People and animals need oxygen to survive. Less oxygen means that fewer animals and people can survive. More carbon dioxide in the air is linked to increased temperatures on earth which can cause animals that are intolerant of temperature increases to either migrate towards higher elevation or the poles where it is cooler or go extinct. More carbon dioxide raises temperatures because carbon dioxide is a greenhouse gas, meaning it traps heat that is reradiated from the ground.

16. The removal of trees can cause erosion. Tree roots stabilize the soil
The removal of trees can cause erosion. Tree roots stabilize the soil. It the trees are removed, the frequent rains of the equator will wash away the soil. This soil will end up in bodies of water and can cause eutrophication because the runoff carries soil with nutrients which can cause algae to grow quickly and die. The fast growth of the algae can block sunlight and cause plants in the water body to die. Bacteria break down the dead organisms removing oxygen from the system thus causing other aquatic organisms to die because of hypoxic conditions.
Soil in the aquatic environment can also cover up riparian habitat that riparian organisms depend on for foraging or nesting. Sediments in the water can also clog fish and invertebrate gills and block light from photosynthesizing plants.
You can also discuss the loss of tourism and aesthetic beauty that the trees provide for people, or the economics of mudslides and the loss of private property, infrastructure or agricultural lands.

17. A radioactive material has a half life of 5 days
A radioactive material has a half life of 5 days. The sample mass was originally 100,000 grams. The mass of the sample is currently 3,125 grams. How old is the sample?

18. 3,125 grams / 100,000 grams = 1/32 1/32 is 5 half lives.
A radioactive material has a half life of 5 days. The sample mass was originally 100,000 grams. The mass of the sample is currently 3,125 grams. How old is the sample?
3,125 grams / 100,000 grams = 1/32
1/32 is 5 half lives.
5 half lives x 5 days = 25 days
Half Life
Parent fraction (radioactive isotope) 1
1/2 2
1/4 3
1/8 4
1/16 5
1/32

19. The sun gives out approximately 1,000 joules per second per square meter at the equator. How much energy will be captured by 4 square meters of rainforest plants in 5 seconds?

20. The sun gives out approximately 1,000 joules per second per square meter at the equator. How much energy will be captured by 4 square meters of rainforest plants in 5 seconds?
1,000 joules /meter2/second x 4 meter2 x 5 seconds = 20,000 joules.
Primary producers absorb 1% of the energy from the sun
.01 x 20,000 joules = 200 joules.

21. Of that 200 joules absorbed by the plants, how much energy can be transferred to a secondary consumer like a jaguar?

22. Of that 200 joules absorbed by the plants, how much energy can be transferred to a secondary consumer like a jaguar?
10 % of energy gets to primary consumers and 10% of that energy gets to secondary consumers.
200 joules x 0.1 = 20 joules
20 joules x .01 = 2 joules.

23. A population of desert tortoise has a growth rate of 3 percent
A population of desert tortoise has a growth rate of 3 percent. How many years will it take that population to double?

24. A population of desert tortoise has a growth rate of 3 percent
A population of desert tortoise has a growth rate of 3 percent. How many years will it take that population to double?
Use the rule of 70.
70/3 = 23.3 years.